Question

identifying types of lines in three dimensions
which are lines that will intersect
which are perpendicular lines?
which are skew lines?

Explanation:

Step1: Recall definitions

• Intersecting lines: Lines that meet at a point.
• Perpendicular lines: Lines that intersect at a right - angle (\(90^{\circ}\)).
• Skew lines: Non - parallel, non - intersecting lines in 3 - D space.

Step2: Analyze \(a\) and \(b\)

• \(a\) and \(b\) are in the same plane (\(N\)), they intersect at a right - angle. So they are perpendicular and intersecting.

Step3: Analyze \(a\) and \(c\)

• \(a\) is in plane \(N\), \(c\) is in another plane. They are non - parallel and non - intersecting. So they are skew.

Step4: Analyze \(b\) and \(c\)

• \(b\) is in plane \(N\), \(c\) is in another plane. They are non - parallel and non - intersecting. So they are skew.

Answer:

• Intersecting and perpendicular: \(a\) and \(b\)
• Skew: \(a\) and \(c\), \(b\) and \(c\)